Elliptic curve isogeny class 15488.20-f over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-15488.20-f
• Conductor: 15488.20
• Rank: \( 1 \)

Base field \(\Q(\sqrt{-7}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 2 \); class number \(1\).

Elliptic curves in class 15488.20-f over \(\Q(\sqrt{-7}) \)

Isogeny class 15488.20-f contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
15488.20-f1	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -22 a - 22\) , \( 67 a + 11\bigr] \)
15488.20-f2	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 10 a - 15\) , \( -4 a - 19\bigr] \)
15488.20-f3	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -40 a + 55\) , \( 6 a - 33\bigr] \)
15488.20-f4	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 16 a + 28\) , \( -29 a + 91\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph